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12-2019

Comparative Study of Winding Configurations of a Five-Phase Comparative Study of Winding Configurations of a Five-Phase

Flux-Switching PM Machine Flux-Switching PM Machine

Hao Chen

Xiangdong Liu

Ayman M. EL-Refaie

Jing Zhao

Nabeel Demerdash

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Authors Authors Hao Chen, Xiangdong Liu, Ayman M. EL-Refaie, Jing Zhao, Nabeel Demerdash, and Jiangbiao He

Marquette University

e-Publications@Marquette

Electrical and Computer Engineering Faculty Research and Publications/College of Engineering

This paper is NOT THE PUBLISHED VERSION; but the author’s final, peer-reviewed manuscript. The published version may be accessed by following the link in th citation below.

IEEE Transactions on Energy Conversion, Vol. 34, No. 4 (December 2019): 1792-1804. DOI. This article is © Institute of Electrical and Electronic Engineers (IEEE) and permission has been granted for this version to appear in e-Publications@Marquette. Institute of Electrical and Electronic Engineers (IEEE) does not grant permission for this article to be further copied/distributed or hosted elsewhere without the express permission from Institute of Electrical and Electronic Engineers (IEEE).

Comparative Study of Winding Configurations of a Five-Phase Flux-Switching PM Machine

Hao Chen School of Automation, Beijing Institute of Technology, Beijing, China

Xiangdong Liu School of Automation, Beijing Institute of Technology, Beijing, China

Ayman M. EL-Refaie Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI

Jing Zhao School of Automation, Beijing Institute of Technology, Beijing, China

Nabeel A. O. Demerdash Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI

Jiangbiao He Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY

Abstract: This paper introduces a general method for determination of the most suitable winding configurations for five-phase flux-switching permanent magnet (FSPM) machines, associated with feasible stator/rotor-pole combinations. Consequently, the effect of winding configurations on the performance of a five-phase outer-rotor FSPM machine is thoroughly investigated, including non-overlapping concentrated windings (single-layer, double-layer, and multi-layer) as well as distributed winding. The electromagnetic characteristics in the low-speed region, the flux-weakening capability in the high-speed region, and the fault-tolerant capability under faulty situations are evaluated and compared in detail. This work shows that compared with the conventional single-layer or double-layer concentrated windings, the FSPM machine with multi-layer type winding exhibits lower torque ripple and losses. Meanwhile, the motor with distributed windings possesses higher torque density and larger inductance. Finally, a prototype is manufactured, and the analysis results are validated by experiments.

Keywords Windings, Stator windings, Traction motors, Torque, Rotors, Brushless motors

SECTION I. Introduction With the increasing concerns on environmental protection and energy security, electric vehicles (EVs) have been widely recognized as a promising candidate to offer an ultimate solution for clean-energy personal mobility [1], [2]. By placing motors in the wheels, the advantages of flexibility and simplicity make the in-wheel traction preferable for EV applications [3].

Instead of conventional permanent magnet (PM) brushless motors with surface-mounted or interior PMs on the rotor, stator-PM machines have attracted considerable attention in this application due to their robust and simple rotor, as well as their favorable PM thermal dissipation [4], [5]. Among the stator-PM motors, flux-switching PM (FSPM) machines exhibit higher torque capability and power density than doubly-salient and flux-reversal PM machines due to the flux-concentration effect [4]. Recently, various topologies have been introduced for FSPM machines, including original [6], hybrid excited [7], partitioned stator [8], and multi-tooth FSPM machines [9], etc. However, most of these machines are limited to normal three-phase inner-rotor system, even though the multi-phase (>3) motors have exhibited better fault-tolerant capabilities and lower torque ripples [10], [11]. Moreover, outer-rotor motors are desirable for in-wheel traction applications because of their low audible noise, compact constructions, and high transmission efficiency with gearless operation [12]. Accordingly, a five-phase outer-rotor FSPM machine is analyzed and investigated in this paper.

The traditional FSPM machine comprises a robust rotor which is identical to that of switched reluctance motors, and a rather complex stator. The stator contains laminated “U”-shaped segments, between which circumferentially magnetized magnets are sandwiched with alternative opposite polarity, over which the “U”-shaped segments are wound by fractional-slot concentrated windings (FSCWs) [13]. FSCW PM motors have been gaining interest as a result of serval advantages, including high-power density, high efficiency, short end turns, and high slot fill factor [14]. However, FSPM machines with FSCWs suffer from high losses by the ill-influence of the presence of both sub- and super-harmonic components in the stator magnetomotive force (MMF). In order to reduce the stator MMF harmonics, reference [15] proposed a method by increasing the number of layers in the stator winding. Consequently, the effects of number of layers on performance of interior PM motors were investigated in [16] and [17]. These investigations indicated that by going to higher number of layers, the efficiency, especially in the high-speed region, and the torque density are significantly improved. Multi-layer

windings have been implemented in FSPM machines with 12/11 stator/rotor-pole [18] and 12/13-pole [19], respectively. These works show that compared with the conventional double-layer configuration, the motors with four-layer windings have lower losses and lower torque ripples. On the other hand, FSPM machines have not been limited to concentrated windings. In [20] and [21], 6/14-pole and 24/16-pole FSPM machines with distributed windings were introduced, and proved that the FSPM machines with distributed windings have higher torque density than their concentrated winding counterparts. A 12/7-pole FSPM machine with full-pitched distributed winding is discussed in [22] and [23], this machine shows lower cogging torque and larger inductance compared with the conventional 12/10-pole FSPM concentrated winding machine. New winding configuration possibilities have been attempted for FSPM machines [24]–[25][26]. However, the prior literatures mostly focus on few stator/rotor-pole combinations. A general method to determine the winding configuration of FSPM machines still is lacking. In addition, comprehensive comparisons between these various winding configurations have not been made.

This paper presents new contributions to the specific subject by comparing the performances of FSPM machines with different winding configurations, i.e., both concentrated windings (single-layer, double-layer, and multi-layer) and distributed wingdings. The overall performances are evaluated including the electromagnetic characteristics in the low-speed region, the flux-weakening capability in the high-speed region, and the fault-tolerant capability under faulty situations. Other new aspects of interest are the determination of the most suitable winding configuration for the five-phase FSPM machine, associated with feasible stator/rotor-pole combinations, novel multi-layer winding topologies for FSPM machines, and the concept of spokes per phase for FSPM machines which is different from other methods previously presented in literature [29] as will be discussed later. Also, the analysis is supported by experimental results.

SECTION II. Design of Balanced Symmetrical Windings For an 𝑚𝑚-phase FSPM machine with balanced and symmetrical windings, based on the “magnetic gear effect”, the relationship between the PM pole-pair number, 𝑃𝑃𝑝𝑝𝑝𝑝, the armature winding pole-pair number, 𝑃𝑃𝑎𝑎𝑎𝑎, and the number of rotor poles, 𝑁𝑁𝑟𝑟, is as follows [27]:

𝑃𝑃𝑝𝑝𝑝𝑝 + 𝑃𝑃𝑎𝑎𝑎𝑎 = 𝑁𝑁𝑟𝑟𝑃𝑃𝑝𝑝𝑝𝑝 = 𝑁𝑁𝑠𝑠/2 (1)(2)

where, 𝑁𝑁𝑠𝑠 is the number of stator poles (teeth). It should be noted that the number, 𝑁𝑁𝑠𝑠, must be even, and the number, 𝑁𝑁𝑟𝑟, in FSPM machines is equivalent to the number of pole pairs rather than poles in conventional rotor-PM machines. In addition, such machines exhibit potential unbalanced magnetic force (UMF) when Nr is an odd number. In these machines, the machine periodicity, 𝜏𝜏, is defined as,

𝜏𝜏 = 𝐺𝐺𝐺𝐺𝐺𝐺(𝑁𝑁𝑠𝑠 ⋅ 𝑘𝑘𝑙𝑙/2,𝑃𝑃𝑎𝑎𝑎𝑎) (3)

where, GCD is greatest common divisor, 𝑘𝑘𝑙𝑙 = 1 for a single-layer winding, while 𝑘𝑘𝑙𝑙 = 2 for a double-layer winding. The star of slots in one basic repeating unit (an equivalent machine with the least slots and poles) is characterized by [𝑁𝑁𝑠𝑠 ⋅ 𝑘𝑘𝑙𝑙/(2𝜏𝜏)] spokes, in which each spoke contains 𝜏𝜏 phasors. Hence, the feasible combination of 𝑁𝑁𝑠𝑠 and 𝑁𝑁𝑟𝑟 should satisfy,

𝑁𝑁𝑠𝑠 2𝜏𝜏⁄ = 𝑚𝑚𝑘𝑘, where 𝑘𝑘 = 1,2, … (4)

Instead of the concept of slots per pole per phase in conventional rotor-PM machines, the spokes per phase in FSPM machines, 𝑞𝑞𝑝𝑝ℎ, is defined as follows:

𝑞𝑞𝑝𝑝ℎ = 𝑁𝑁𝑠𝑠 ⋅ 𝑘𝑘𝑙𝑙/(2𝜏𝜏 ⋅ 𝑚𝑚) (5)

The electrical slot-pitch angle is given by,

𝛼𝛼𝑒𝑒 = 𝑃𝑃𝑎𝑎𝑎𝑎 ⋅ (2𝜋𝜋/𝑁𝑁𝑠𝑠) (6)

while the angle between two adjacent spokes is given by,

𝛼𝛼𝑠𝑠 = 2𝜋𝜋/[𝑁𝑁𝑠𝑠 ⋅ 𝑘𝑘𝑙𝑙/(2𝜏𝜏)] (7)

The winding factor, 𝑘𝑘𝑎𝑎, is expressed according to [28] as follows:

𝑘𝑘𝑎𝑎 = 𝑘𝑘𝑑𝑑 ⋅ 𝑘𝑘𝑝𝑝

𝑘𝑘𝑑𝑑 = �sin (

𝑞𝑞𝑝𝑝ℎ2

⋅𝛼𝛼𝑠𝑠2

)/[𝑞𝑞𝑝𝑝ℎ

2⋅ sin (

𝛼𝛼𝑠𝑠2

)], if 𝑞𝑞𝑝𝑝ℎ is even

sin (𝑞𝑞𝑝𝑝ℎ ⋅𝛼𝛼𝑠𝑠4

)/[𝑞𝑞𝑝𝑝ℎ ⋅ sin (𝛼𝛼𝑠𝑠4

)], if 𝑞𝑞𝑝𝑝ℎ is odd

𝑘𝑘𝑝𝑝 = sin �𝑦𝑦 ⋅ 𝛼𝛼𝑒𝑒

2�

where, 𝑘𝑘𝑑𝑑 is the distribution factor, 𝑘𝑘𝑝𝑝 is the pitch factor, and 𝑦𝑦 is the coil pitch, measured in number of slots.

The non-overlapping concentrated windings (NCWs) are preferable in conventional FSPM machines due to their short end turns. Nevertheless, the overlapping windings are also investigated in this paper.

SECTION A. Non-Overlapping Concentrated Windings NCWs whose coil pitch is one (𝑦𝑦 = 1) include single-layer windings, double-layer windings, and multi-layer windings (here, these are represented by four-layer windings). These topologies will be analyzed and compared for a five-phase outer-rotor FSPM machine with 20/21 stator/rotor-pole as shown in Fig. 1(a), (b), and (c), respectively. In addition, a 10/21-p FSPM machine with double-layer winding is depicted in Fig. 1(d) for further stator/rotor-pole combination analysis. Their corresponding stars of slots are illustrated in Fig. 2(a), (b), (c), and (d), respectively.

Fig. 1. (a) 20/21-p PSPM machine with single-layer winding. (b) Double-layer winding. (c) Four-layer winding. (d) 10/21-p FSPM machine with double-layer winding.

Fig. 2. Star of slots. (a) 20/21-p PSPM machine with single-layer winding. (b) Double-layer winding. (c) Four-layer winding. (d) 10/21-p FSPM machine with double-layer winding.

It is interesting to note that with introducing the concept of an armature winding pole-pair number, 𝑃𝑃𝑎𝑎𝑎𝑎, into FSPM machines, though it is not equal to its magnet pair number as in regular rotor-PM motors, there is no need to take the polarity of coils into consideration when determining the winding connection. This method is quite different from, but much more convenient than that introduced in early works [29], [30]. For example, the two coils of phase A in 20/21-p machine with single-layer winding are in two different sectors, labeled A+ and A− as shown in Fig. 2(a). Therefore, these coils should be in series-opposing connection as shown in Fig. 3(a), while those coils in a 10/21-p machine with double-layer winding are in the same sector, labeled A as shown in Fig. 2(d), and accordingly they are in series-aiding connection as shown in Fig. 3(b). This is coincident with those polarities depicted in Fig. 1(a) and (d), respectively.

Fig. 3. Winding connection. (a) Series-opposing. (b) Series-aiding.

The back electromotive force (EMF) waveform of a single coil may be asymmetrical in FSPM machines due to the nature of the asymmetric magnetic flux paths as the rotor rotates. While, if the machine consists of one or more pairs of coils per phase whose magnetic flux paths having a phase shift of 180 electrical degrees, the even harmonics cancel each other and the phase back-EMF will be symmetrical [29]. Hence, for 𝑚𝑚-phase (𝑚𝑚 is odd) FSPM machines, there are two cases which can achieve symmetrical phase back-EMF waveform: (1) If 𝑞𝑞𝑝𝑝ℎ is even, the number of rotor poles per basic repeating unit should be odd, and (2) If 𝑞𝑞𝑝𝑝ℎ is odd, τ must be even, and the number of rotor poles for two basic repeating units should be odd. Thus, the condition for symmetrical phase back-EMF is summarized as follows:

(𝑞𝑞𝑝𝑝ℎ is even) ∩ (𝑁𝑁𝑠𝑠/𝜏𝜏 is odd)(𝑞𝑞𝑝𝑝ℎ is odd) ∩ (𝜏𝜏 is odd) ∩ (2𝑁𝑁𝑠𝑠/𝜏𝜏 is odd)� (11)

In single-layer winding machines, each slot is occupied by the coil side of a single phase [Fig. 1(a)]. The main winding parameters of five-phase single-layer winding FSPM machines with some feasible stator/rotor pole combinations are listed in Table I (# and * mean that the phase back-EMF waveform is asymmetrical for 10 stator-pole and 20 stator-pole machines, respectively). As can be seen, all of the phase back-EMF waveforms of the motors with 10 stator-poles are asymmetrical, while those machines with 20 stator-poles and odd rotor poles are symmetrical. In addition, when 𝑁𝑁𝑟𝑟 is close to (𝑘𝑘 ⋅ 𝑁𝑁𝑠𝑠), e.g., 10/11-p, 10/21-p, 20/21-p, those machines exhibit a larger winding factor, resulting in higher torque density.

TABLE I Main Winding Parameters of Single-Layer Winding FSPM Machines 𝑁𝑁𝑠𝑠 𝑁𝑁𝑟𝑟 6# 7# 8# 9# 11# 12# 13#

10 𝑃𝑃𝑎𝑎𝑎𝑎 1 2 3 4 6 7 8 𝜏𝜏 1 1 1 1 1 1 1 𝑞𝑞𝑝𝑝ℎ 1 1 1 1 1 1 1 𝑘𝑘𝑑𝑑 1 1 1 1 1 1 1 𝑘𝑘𝑞𝑞 0.309 0.588 0.809 0.951 0.951 0.809 0.588 𝑘𝑘𝑎𝑎 0.309 0.588 0.809 0.951 0.951 0.809 0.588 20 𝑃𝑃𝑎𝑎𝑎𝑎 - 4 - 3 - 2 - 1 1 2 3 𝜏𝜏 N/A N/A N/A N/A 1 2 1 𝑞𝑞𝑝𝑝ℎ N/A N/A N/A N/A 2 1 2 𝑘𝑘𝑑𝑑 N/A N/A N/A N/A 1 1 1 𝑘𝑘𝑞𝑞 N/A N/A N/A N/A 0.156 0.309 0.454 𝑘𝑘𝑎𝑎 N/A N/A N/A N/A 0.156 0.309 0.454 𝑁𝑁𝑠𝑠 𝑁𝑁𝑟𝑟 14#,* 16#,* 17#,* 18#,* 19#,* 21#,* 22#,*

10 𝑃𝑃𝑎𝑎𝑎𝑎 9 11 12 13 14 16 17 𝜏𝜏 1 1 1 1 1 1 1 𝑞𝑞𝑝𝑝ℎ 1 1 1 1 1 1 1 𝑘𝑘𝑑𝑑 1 1 1 1 1 1 1 𝑘𝑘𝑞𝑞 0.309 0.309 0.588 0.809 0.951 0.951 0.809 𝑘𝑘𝑎𝑎 0.309 0.309 0.588 0.809 0.951 0.951 0.809 20 𝑃𝑃𝑎𝑎𝑎𝑎 4 6 7 8 9 11 12 𝜏𝜏 2 2 1 2 1 1 2 𝑞𝑞𝑝𝑝ℎ 1 1 2 1 2 2 1 𝑘𝑘𝑑𝑑 1 1 1 1 1 1 1 𝑘𝑘𝑞𝑞 0.588 0.809 0.891 0.951 0.988 0.988 0.951 𝑘𝑘𝑎𝑎 0.588 0.809 0.891 0.951 0.988 0.988 0.951

In double-layer winding machines, each slot is split equally for two coil sides from one or two phases [Fig. 1(b)]. The main winding parameters are listed in Table II. As can be seen, all machines with 𝑞𝑞𝑝𝑝ℎ ≠ 2 can achieve symmetrical phase back-EMF. Therefore, in terms of symmetrical phase back-EMF, the feasible stator/rotor-pole combinations for machines with double-layer winding are much more than those with single-layer winding.

TABLE II Main Winding Parameters of Double-Layer Winding Machines 𝑁𝑁𝑠𝑠 𝑁𝑁𝑟𝑟 6# 7 8# 9 11 12#,* 13

10 𝜏𝜏 1 2 1 2 2 1 2 𝑞𝑞𝑝𝑝ℎ 2 1 2 1 1 2 1 𝑘𝑘𝑑𝑑 1 1 1 1 1 1 1 𝑘𝑘𝑞𝑞 0.309 0.588 0.809 0.951 0.951 0.809 0.588 𝑘𝑘𝑎𝑎 0.309 0.588 0.809 0.951 0.951 0.809 0.588 20 𝜏𝜏 N/A N/A N/A N/A 1 2 1 𝑞𝑞𝑝𝑝ℎ N/A N/A N/A N/A 4 2 4 𝑘𝑘𝑑𝑑 N/A N/A N/A N/A 0.988 1 0.988 𝑘𝑘𝑞𝑞 N/A N/A N/A N/A 0.156 0.309 0.454

𝑘𝑘𝑎𝑎 N/A N/A N/A N/A 0.155 0.309 0.448 𝑁𝑁𝑠𝑠 𝑁𝑁𝑟𝑟 14#,* 16#,* 17 18# 19 21 22#

10 𝜏𝜏 1 1 2 1 2 2 1 𝑞𝑞𝑝𝑝ℎ 2 2 1 2 1 1 2 𝑘𝑘𝑑𝑑 1 1 1 1 1 1 1 𝑘𝑘𝑞𝑞 0.309 0.309 0.588 0.809 0.951 0.951 0.809 𝑘𝑘𝑎𝑎 0.309 0.309 0.588 0.809 0.951 0.951 0.809 20 𝜏𝜏 4 2 1 4 1 1 4 𝑞𝑞𝑝𝑝ℎ 1 5 4 1 4 4 1 𝑘𝑘𝑑𝑑 1 1 0.988 1 0.988 0.988 1 𝑘𝑘𝑞𝑞 0.588 0.809 0.891 0.951 0.988 0.988 0.951 𝑘𝑘𝑎𝑎 0.588 0.809 0.880 0.951 0.976 0.976 0.951

Multi-layer winding machines comprise more than two coil sides per slot, and accordingly, a four-layer winding is considered in this paper. Compared with the counterpart of the machine with double-layer winding, the sectors of the machine in the star of slots with four-layer winding are doubled. As shown in Fig. 2(c), each phase has two positive and two negative sectors, e.g., sector A+, A++, and A−, A−. The second set of sectors, A++ and A−, is shifted by an angle 𝛼𝛼𝑠𝑠ℎ4, which is decided by the structure of the specific machine to obtain a maximum winding factor. Hence, the winding factor is computed based on that of the two-layer winding as,

𝑘𝑘𝑎𝑎4 = 𝑘𝑘𝑎𝑎2 ⋅ cos (𝛼𝛼𝑠𝑠ℎ4/2) (12)

where, 𝑘𝑘𝑎𝑎4 and 𝑘𝑘𝑎𝑎2 are the four-layer and double-layer winding factor, respectively. The purpose of the multi-layer winding topology is to reduce both the sub- and super-stator MMF harmonics based on the advantage of spatial misalignment, so that the back-EMF waveform will be closer to sinusoidal. For instance, the back-EMF waveforms and their harmonic content of the 10/22-p FSPM machines with both double-layer and four-layer windings are shown in Fig. 4(a) and (b), respectively. The two machines have the same outer diameter, stack length, air-gap height, and number of turns per phase. As can be seen, the total harmonic distortion (THD) is significantly reduced from 17.17% with double-layer winding to 11.25% with four-layer winding, with a slight decrease of the fundamental component due to the winding factor given in eq. (12). This verified the previous analysis results. Moreover, it is interesting to note that, for 10 stator-pole machines with double-layer winding in Table II, the machines with odd number of rotor-poles can achieve symmetrical phase back-EMF, but suffer from UMF. By contrast, there is no UMF in even rotor-pole machines, but their phase back-EMFs are asymmetrical. Therefore, the four-layer winding concept offers good tradeoff between the back-EMF waveform and UMF for the 10 stator poles, even number rotor poles FSPM machines.

Fig. 4. Back-EMF of the 10/22-p FSPM machine. (a) Back EMF waveforms. (b) Harmonic spectrum.

B. Distributed Windings The winding factor is an index of the goodness of the winding configuration, since it is proportional to the torque density. As can be observed in Table I and Table II, with NCWs, there are only a limited number of stator/rotor-pole combinations which can provide a relatively large winding factor, such as 10/11-p, 10/21-p, and 20/21-p. Furthermore, even with these combinations, the theoretical maximum value ((𝑘𝑘𝑎𝑎 = 1)) is unattainable unless 𝑁𝑁𝑟𝑟 = 𝑘𝑘·𝑁𝑁𝑠𝑠, according to eq. (6) and eq. (10), which is infeasible due to the relationship in eq. (4). The main reason of low winding factors for the other combinations is the relatively low pitch factor, governed by eq. (10). Distributed windings can solve this problem.

In distributed winding machines, each coil is wound around more than one stator tooth, i.e., 𝑦𝑦 > 1, thus the coils will overlap each other. In general, the full-pitched winding is selected due to their maximum pitch factor. Hence, a full-pitched distributed winding configuration is proposed and applied to a 20/31-p FSPM machine as shown in Fig. 5(b), while its counterpart with non-overlapping concentrated winding (single-layer) is shown in Fig. 5(a). Their corresponding stars of slots are illustrated in Fig. 6. Their main winding parameters are listed in Table III. The back-EMF waveforms and their harmonic content of the two motors are shown in Fig. 7(a) and (b), respectively. As can be seen, for the motor with non-overlapping concentrated winding, the pitch factor, 𝑘𝑘𝑞𝑞, is as low as 0.156, even though its distribution factor, 𝑘𝑘𝑑𝑑, is unit. While the winding factor of the motor with distributed winding is significantly improved from 0.156 to 0.988. In addition, by adopting a full-pitched distributed winding, the fundamental component of the back-EMF is increased by 6.31 times from 7.77 V to 49.02 V, which fairly matches the ratio between the winding factors of the two motors.

Fig. 5. Armature winding connection of the 20/31-p FSPM machine. (a) Conventional non-overlapping winding. (b) Distributed winding.

Fig. 6. Star of slots of the 20/31-p FSPM machine. (a) Conventional non-overlapping winding. (b) Distributed winding.

TABLE III Main Winding Parameters of the 20/31-p FSPM Machine 𝑡𝑡 𝑞𝑞𝑝𝑝ℎ 𝑦𝑦 𝑎𝑎𝑒𝑒 𝑎𝑎𝑠𝑠 𝑘𝑘𝑑𝑑 𝑘𝑘𝑞𝑞 𝑘𝑘𝑎𝑎 Concentrated 1 2 1 18 36 1 0.156 0.156 Distributed 1 2 10 18 18 0.988 1 0.988

Fig. 7. Back-EMF of the 20/31-p FSPM machine. (a) Back EMF waveforms. (b) Harmonic spectra.

SECTION III. Comparison and Discussion To comprehensively evaluate the performances of the five-phase outer-rotor FSPM machine with different winding configurations, four different winding topologies are selected and compared in this section, namely, 20/21-p machine with non-overlapping concentrated single-layer winding [Fig. 1(a)], double-layer winding [Fig. 1(b)], four-layer winding [Fig. 1(c)], and a 20/31-p machine with full-pitched distributed winding [Fig. 5(b)], respectively. For a fair comparison, some parameters of the four machines were kept the same as listed in Table IV. It should be noted that the rated electric frequencies are identical (217 Hz) for the four machines, thus, the rated speed is 620 r/min for the 20/21-p machines, while it is 420 r/min for the 20/31-p machine.

TABLE IV Parameters of the Four Investigated Machines

Parameter Value Parameter Value Rated phase current (A) 10 Stator inner radius (mm) 49 Rated frequency (Hz) 217 Stack length (mm) 85 Rotor outer radius (mm) 112.5 Number of turns /phase 96 Rotor inner radius (mm) 88.5 PM remanence NdfeB (T) 1.23 Air-gap length (mm) 0.5 PM volume (mm3) 16500

A. Performance in Low-Speed Region In low-speed region, motors in EV applications require good torque characteristics, average torque and overload capability, to provide enough acceleration, low cogging torque and torque ripple to reduce acoustic noise and vibration, high power factor and efficiency to save energy.

The flux density distribution of the four motors are depicted in Fig. 8(a), (b), (c), and (d), respectively. The open-circuit radial air-gap flux density profiles are shown in Fig. 9. It should be noted that for the three non-overlapping concentrated winding machines, the only difference is the winding configuration, therefore, the performances of the three machines under open-circuit condition are the same. It can be seen that in all cases, the air-gap flux density is non-sinusoidal and the peak values are as high as 2T in the vicinity of aligned stator and rotor poles due to the flux-concentration effect.

Fig. 8. Flux density distribution of the four motors. (a) 20/21-p machine with single-layer winding. (b) Double-layer winding. (c) Four-layer winding. (d) 20/31-p machine with distributed winding.

Fig. 9. Radial air-gap flux density.

The no-load back-EMF waveforms of the four machines and their harmonic spectra are shown in Fig. 10. As can be seen, all the four back-EMF waveforms are symmetrical. For the NCWs, although the back-EMF waveforms of the three machines are quite similar, the amplitudes of the harmonics and the THD are reduced from single to double to four-layer winding configurations. In addition, the fundamental component of the back-EMF of the machine with full-pitched distributed winding is the largest.

Fig. 10. No-load back-EMF (20/21-p @ 620 r/min, 20/31-p @ 420 r/min). (a) Back EMF waveforms. (b) Harmonic spectra.

Some main parameters at rated condition are summarized in Table V, where, 𝜓𝜓𝑝𝑝 is the rms flux linkage due to the PMs, 𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐 is the cogging torque, 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐 is the average torque, 𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒 is the torque ripple, 𝑃𝑃𝑓𝑓 is the power factor, 𝑃𝑃𝑐𝑐𝑐𝑐 is the copper loss, 𝑃𝑃𝑐𝑐𝑐𝑐𝑟𝑟𝑒𝑒 is the core loss, 𝑃𝑃𝑃𝑃𝑃𝑃 is the PM eddy-current loss, η is the efficiency. It was found that for the NCWs, a higher number of winding layers tends to reduce the sub- and super-harmonics, which reduces the torque ripple, core loss and PM eddy-current loss, therefore, improves the efficiency, with a little sacrifice of the PM flux linkage and average torque. Compared to the NCWs, the machine with distributed winding shows the largest PM flux linkage and average torque, but it possesses higher torque ripple and lower efficiency due to its rich stator MMF harmonics, moreover, its power factor is the lowest. In addition, the 20/21-p machines have a larger cogging torque than that of the 20/31-p one, because of the relationship between the cogging torque and the GCD of 𝑁𝑁𝑠𝑠 and 𝑁𝑁𝑟𝑟 [31].

TABLE V Performance of the Four FSPM Machines Single-layer Double-layer Four-layer Distributed 𝛹𝛹𝑝𝑝(Wb) 0.0485 0.0480 0.0473 0.0541 𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐(Nm) 0.52 0.52 0.52 0.32 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐(Nm) 50.22 49.89 49.26 66.96 𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒(%) 4.51 3.32 3.10 5.87 𝑃𝑃𝑓𝑓 0.938 0.965 0.959 0.316 𝑃𝑃𝑐𝑐𝑐𝑐(W) 90.13 83.40 83.40 227.56 𝑃𝑃𝑐𝑐𝑐𝑐𝑟𝑟𝑒𝑒(W) 118.09 112.59 108.28 227.30 𝑃𝑃𝑃𝑃𝑃𝑃(W) 85.23 82.09 80.77 164.00 𝜂𝜂(%) 91.74 92.09 92.15 82.63

The overload capability is imperative for motors in EV applications, especially in hill-climbing and acceleration operations. Hence, the torque-current characteristics of the four machines are compared in Fig. 11. It shows that the variation of the torque versus current of the machines with double-layer and four-layer windings are almost the same, while they have better torque capability in the high q-axis current, 𝑖𝑖𝑞𝑞, region than that of the single-layer winding one. By contrast, the torque of the distributed winding machine is higher in the low 𝑖𝑖𝑞𝑞 region, but much smaller in the high 𝑖𝑖𝑞𝑞 region than that of its NCW counterparts. This can be explained by the torque equation given by,

𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐 = 52𝑁𝑁𝑟𝑟𝜓𝜓𝑝𝑝𝑖𝑖𝑞𝑞 (13)

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Fig. 11. Variation of torque versus current for the four machines.

There is no reluctance torque component because the difference between the d- and q-axis inductances is negligible which will be verified next. Therefore, all the four FSPM machines operate under zero d-axis current ((𝑖𝑖𝑑𝑑 = 0)) mode in this investigation. The PM flux linkage, 𝜓𝜓𝑝𝑝, is influenced by the 𝑖𝑖𝑞𝑞 as shown in Fig. 12. It can be seen that with the 𝑖𝑖𝑞𝑞 increasing, the PM flux linkage, 𝜓𝜓𝑝𝑝, of the distributed winding machine drops more sharply due to the more significant demagnetizing armature reaction effect caused by 𝑑𝑑- and 𝑞𝑞-axis cross-coupling, therefore, its torque saturates more quickly. However, the 𝜓𝜓𝑝𝑝 of the NCW machines decreases slightly during the entire range, showing a stronger anti-saturation ability, and thus high overload capability.

Fig. 12. D-axis PM flux linkage versus q-axis current.

B. Flux-Weakening Capability in High-Speed Region For traction applications, the flux-weakening capability is of particular importance since it determines the loading capability and constant power speed range in the high-speed region. The flux weakening can be explained as follows:

Using Clarke and Park transformation, the five-phase quantities can be converted to two-phase, namely, 𝑑𝑑 and 𝑞𝑞 quantities as follows:

𝑉𝑉𝑑𝑑 = 𝑅𝑅𝑖𝑖𝑑𝑑 − 𝜔𝜔𝑒𝑒𝐿𝐿𝑞𝑞𝑖𝑖𝑞𝑞𝑉𝑉𝑞𝑞 = 𝑅𝑅𝑖𝑖𝑞𝑞 +𝜔𝜔𝑒𝑒(𝜓𝜓𝑝𝑝 + 𝐿𝐿𝑑𝑑𝑖𝑖𝑑𝑑)𝑖𝑖𝑠𝑠2 = 𝑖𝑖𝑑𝑑2 + 𝑖𝑖𝑞𝑞2 ≤ 𝑖𝑖𝑝𝑝𝑎𝑎𝑚𝑚

2

𝑉𝑉2 = 𝑉𝑉𝑑𝑑2 + 𝑉𝑉𝑞𝑞2 ≤ 𝑉𝑉𝑝𝑝𝑎𝑎𝑚𝑚2

where, 𝑉𝑉𝑑𝑑, 𝑉𝑉𝑞𝑞 and 𝐿𝐿𝑑𝑑, 𝐿𝐿𝑞𝑞 are the 𝑑𝑑- and 𝑞𝑞-axis voltages and inductances, 𝑅𝑅 is the phase resistance, 𝜔𝜔𝑒𝑒 is the electrical angular frequency velocity, 𝑖𝑖𝑠𝑠 is the rated stator phase current, 𝑉𝑉 is the phase terminal voltage, 𝑖𝑖𝑝𝑝𝑎𝑎𝑚𝑚 and 𝑉𝑉𝑝𝑝𝑎𝑎𝑚𝑚 are the current and voltage limits. In principle, the terminal voltage, 𝑉𝑉, is almost proportional to the rotational speed below the base speed, 𝑛𝑛𝑏𝑏. As speed increases above 𝑛𝑛𝑏𝑏, the flux-weakening control mode should be implemented by adjusting the phase angle of 𝑖𝑖𝑠𝑠, and as a result, the 𝜓𝜓𝑝𝑝 is reduced to some extent by the negative 𝑖𝑖𝑑𝑑, so that the voltage will be kept within its limit. Hence, the flux-weakening coefficient, 𝑘𝑘𝑓𝑓𝑎𝑎, is defined to quantify the flux-weakening capability as follows:

𝑘𝑘𝑓𝑓𝑎𝑎 = 𝐿𝐿𝑑𝑑𝑖𝑖𝑠𝑠/𝜓𝜓𝑝𝑝 (18)

Table VI reports the flux-weakening performance of the four machines. As can be seen, all saliency ratios ((𝐿𝐿𝑞𝑞/𝐿𝐿𝑑𝑑)) of the four machines are less than 1.2 pu, which is the reason why the reluctance toque is neglected in eq. (13). Moreover, the flux-weakening coefficients, 𝑘𝑘𝑓𝑓𝑎𝑎, of the machines with double- and four-layer windings are smaller than that of the single-layer winding machine. This is due to their smaller 𝐿𝐿𝑑𝑑. It should be noted that the characteristic current, 𝐼𝐼𝑐𝑐ℎ = 𝜓𝜓𝑝𝑝/𝐿𝐿𝑑𝑑, of the machines with concentrated winding is higher than the rated current of 10 A and hence they have a cutoff speed/limited constant power speed range. While in case of the machine with distributed winding, the characteristic current, 𝐼𝐼𝑐𝑐ℎ, is lower than the rated current and hence it has the capability to achieve a wide constant power range but at a reduced level proportional to the ratio of the machine characteristic current to the machine rated current [32], [33]. The torque and power versus speed at the limit voltage of the four machines are shown in Fig. 13. As can be seen, the machine with the distributed winding has the largest torque capability in the low-speed region if the rated current of 10A is applied, while it has the best flux-weakening capability in the high-speed region if the reduced current is applied. Hence, the distributed winding machine has better flexibility to operate throughout the entire speed range.

TABLE VI Flux-Weakening Performance of the Four FSPM Machines Single-layer Double-layer Four-layer Distributed 𝑛𝑛𝑏𝑏(r/min) 620 620 620 420 𝑉𝑉𝑝𝑝𝑎𝑎𝑚𝑚(V) 75.80 72.86 72.37 225.22 𝐿𝐿𝑑𝑑(mH) 2.01 1.61 1.68 15.65 𝐿𝐿𝑞𝑞(mH) 2.32 1.87 1.94 15.79 𝐿𝐿𝑞𝑞/𝐿𝐿𝑑𝑑 1.154 1.161 1.155 1.009 𝑘𝑘𝑓𝑓𝑎𝑎 0.41 0.33 0.35 2.89

Fig. 13. Flux-weakening capability of the four motors. (a) Torque vs. speed. (b) Power vs. speed.

C. Fault-Tolerant Capability Fault-tolerant technology is crucial for the post-fault continued operation of the motor, especially for safety-critical applications. Inductances are good indicators to quantify the fault-tolerant capability. Hence, the inductances of the four machines are listed in Table VII, where, 𝐿𝐿𝐴𝐴𝐴𝐴 is the self-inductance, 𝐿𝐿𝐴𝐴𝐴𝐴, 𝐿𝐿𝐴𝐴𝐴𝐴, 𝐿𝐿𝐴𝐴𝐴𝐴, and 𝐿𝐿𝐴𝐴𝐴𝐴 are the mutual inductances which are presented as a percentage of 𝐿𝐿𝐴𝐴𝐴𝐴. It shows that with the number of layers increasing in the NCW machines (single-layer, double-layer, and four-layer), the self-inductance decreases. While the distributed winding machine has both the largest self-inductance and mutual inductances, due to its largest permeance caused by its largest flux cross-sectional area and hence it has high flux linkage [21]. It is interesting to note that 𝐿𝐿𝐴𝐴𝐴𝐴 of the four-layer winding machine is smaller than that of its counterpart with double-layer winding, while its d-axis inductance, 𝐿𝐿𝑑𝑑, is larger, and therefore its flux-weakening capability is better, see Table VI. The reason is that the four-layer winding machine has larger mutual inductance.

TABLE VII Inductances of the Four FSPM Machines Inductances Single-layer Double-layer Four-layer Distributed 𝐿𝐿𝐴𝐴𝐴𝐴(mH) 4.00 2.57 2.14 11.76 𝐿𝐿𝐴𝐴𝐴𝐴(¾) 1.75 0.39 0.47 5.36 𝐿𝐿𝐴𝐴𝐴𝐴(%) 10.5 5.06 20.09 30.95 𝐿𝐿𝐴𝐴𝐴𝐴(¾) 10.5 5.06 20.09 30.95 𝐿𝐿𝐴𝐴𝐴𝐴(%) 1.75 0.39 0.47 5.36

The profiles of the short-circuit currents in case of a terminal short circuit for the four machines are shown in Fig. 14. As can be seen, a high number of layers indicate larger short-circuit current amplitudes, while the short-circuit current of the distributed winding machine is the lowest in amplitude. This is consistent with the analysis results of inductances given earlier in Table VII.

Fig. 14. Short-circuit currents versus the variation of the rotor position.

The performance of the four machines under open-circuit faults is investigated here in this paper, including one phase (Phase A), two adjacent phases (Phase A and Phase B), and two non-adjacent phases (Phase A and Phase C) open-circuit faults, respectively. In order to keep the stator MMF constant before and after an open-circuit fault occurs based on the fault-tolerant control strategy in [34], the healthy and post-fault current excitations (amplitude and phase angle) have to be readjusted as listed in Table VIII. The torque characteristics of the machines after implementation of the fault-tolerant control strategy are listed in Table IX, in which, the post-fault average torques, 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐, as a percentage of the healthy value of 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐 are included within the parentheses. As can be seen, for the three NCW machines, a machine with a high number of winding layers exhibits closer average torque under fault to that in its healthy condition. For example, under Phase A and Phase B open-circuit faulty condition, the post-fault average torques are from 74.09% to 87.23% to 91.56% of their healthy average torques for the single-layer to the double-layer to the four-layer winding machines, respectively. In addition, a winding with a high number of layers effectively reduces the torque ripple under open-circuit faults. The distributed winding machine shows worse torque characteristics under fault due to its high self- and mutual inductances. Another reason could be that more serious saturation occurs due to the large post-fault currents. It should be noted that this study is mainly focused on outer-rotor FSPM machines. In order to provide a better understanding of how the winding configurations affect the various machine topologies, four inner-rotor FSPM machines with different winding configurations are also investigated as shown in the Appendix. As can be seen, similar conclusions are drawn as in the case of the outer-rotor FSPM machines.

TABLE VIII Current Excitations of the Machines Under Different Conditions Healthy A open A&B open A&C open A (I, 0) 0 0 0 B (I, -2π/5) (1.382I, -π /5) 0 (1.382I, -2 π /5) C (I, -4π/5) (1.382I, -4n /5) (2.236I, -2 π /5) 0 D (I, -6π/5) (1.382I, 4 π /5) (3.618I, 4 π /5) (2.236I, - π) E (I, -8π/5) (1.382I, π /5) (2.236I, 0) (2.236I, π /5)

TABLE IX Torque Characteristics of the Machines in Faulty Conditions Single-layer Double-layer Four-layer Distributed Healthy 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐(Nm) 50.22 49.89 49.26 66.96 𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒(%) 4.51 3.32 3.10 5.87 A Open 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐(Nm) 48.95 (97.49%) 49.38 (98.98%) 48.82 (99.11%) 60.74 (90.71%) 𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒(%) 15.92 12.29 11.41 45.21 A&B Open 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐(Nm) 37.21 (74.09%) 43.52 (87.23%) 45.10 (91.56%) 49.51 (73.94%) 𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒(%) 67.41 34.60 27.17 74.73 A&C Open 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐(Nm) 45.54 (90.68%) 47.94 (96.09%) 47.96 (97.36%) 54.14 (80.85%)

𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒(%) 34.03 18.22 17.02 53.15

SECTION IV. Experimental Validation So far, the five-phase outer-rotor 10/21-p FSPM machine with E-core stator was manufactured and tested as shown in Fig. 15, while the 20/21-p NCW FSPM machine with different number of winding layers is still under construction. The advantages of the FSPM machine with an E-core stator over its counterpart with traditional U-core stator has been emphasized in [35] and [36].

Fig. 15. Prototype of the Five-phase FSPM Machine. (a) Rotor. (b) Stator.

The phase back-EMF waveform and its harmonic spectra under open circuit condition at 200 r/min is shown in Fig. 16. As can be seen, the measured and finite element (FE) simulated back-EMF waveforms are in acceptable agreement, although the measured back-EMF is 8.25% lower than the 2-D FE-prediction due to end-effect and manufacturing imperfections. In addition, the calculated and measured phase resistance are 0.231 Ω and 0.239 Ω, respectively. They are also in good agreement. These measured results verify the accuracy and validity of the finite element modeling and simulation process presented in this paper.

Fig. 16. (a) Predicted and measured back-EMF of the FSPM machine @ 200 r/min. (b) Harmonic spectra.

SECTION V. Conclusion In this paper, a generic method for winding design of FSPM machines, associated with feasible number of stator/rotor-pole combinations was introduced. Hence, four five-phase outer-rotor FSPM machines with different winding configurations were modeled, investigated, and compared in detail, where various tradeoffs were discussed. Therefore, the following conclusions can be inferred from the results of this work:

With the presented winding design method, by introducing the concepts of armature winding pole-pair number based on the “magnetic gear effect”, there is no need to take the polarity of coils into consideration when configuring the winding connection. It is much more convenient for designers than the methods already presented in the previous literature.

In NCW machines, there are only a limited number of stator/rotor-pole combinations which can provide a relatively large winding factor. Meanwhile, a distributed winding approach can solve this low winding factor problem. A full-pitched distributed winding FSPM machine provides significant improvement regarding winding factor values and the magnitude of the fundamental component of the back-EMF, compared with its counterpart with non-overlapping winding.

In NCW machines, with the number of winding layers increasing, the machine exhibits better back-EMF waveform, less torque ripple and lower losses, higher efficiency, and better fault-tolerant capability under open-circuit faults, but less average torque, less self-inductance and therefore larger short-circuit currents.

Among the four machines compared in Section III of this paper, the double-layer winding machine exhibits the highest power factor and the best overload capability. The four-layer winding machine provides the lowest torque ripple, lowest losses and therefore highest efficiency. Meanwhile, the distributed winding machine has the largest average torque, best flux-weakening capability, and lowest short-circuit current, but highest losses and therefore lowest efficiency, worst overload capability and worst fault-tolerant capability under open-circuit faults. Accordingly, the appropriate tradeoffs should be made when designing/choosing the winding configurations suitable to the specific application under consideration.

ACKNOWLEDGMENT The authors would like to express sincere thanks to ANSYS, Inc. for the software support.

Appendix A Case Study of Inner-Rotor FSPM Machines The main parameters of the four investigated inner-rotor FSPM machines are listed in Table X. It should be noted that the inner-rotor machines and the out-rotor machines have the same physical air-gap (from 88 mm to 88.5 mm). This is because in this way, the inner-rotor machines and the outer-rotor machines can be cut and flatten to be the same linear machines.

TABLE X Parameters of the Four Investigated Inner-Rotor Machines Parameter Value Parameter Value Rated phase current (A) 10 Rotor inner radius (mm) 64 Rated frequency (Hz) 217 Stack length (mm) 85 Stator outer radius (mm) 127.5 Number of turns/phase 96 Stator inner radius (mm) 88.5 PM remanence NdFeB (T) 1.23 Air-gap length (mm) 0.5 PM volume (mm3) 16500

The flux density distribution of the four inner-rotor motors are depicted in Fig. 17. The no-load back-EMF waveforms of the four inner-rotor FSPM machines and their harmonic spectra are shown in Fig. 18. As can be

seen, for the NCW machines, the amplitude of the fundamental harmonic component and the THD are reduced from single to double to four-layer winding configurations. The fundamental component of the back-EMF of the distributed winding machine is the highest. Some main parameters of the four inner-rotor machines at rated condition are listed in Table XI. It was found that for the NCWs, a higher number of winding layers tends to reduce the torque ripple, core loss, and PM eddy-current loss, and therefore, improve the efficiency, with a little sacrifice of the PM flux linkage and average torque. While the distributed winding machine shows the largest PM flux linkage and average torque, but it possesses higher torque ripple and lower efficiency. The torque-current characteristics of the four inner-rotor machines showing the overload capability are depicted in Fig. 19. These results of the inner-rotor FSPM machines are consistent with those of the outer-rotor FSPM machines.

Fig. 17. Flux density distribution of the four inner-rotor motors. (a) 20/21-p machine with single-layer winding. (b) Double-layer winding. (c) Four-layer winding. (d) 20/31-p machine with distributed winding.

Fig. 18. No-load back-EMF of the four inner-rotor machines (20/21-p @ 620 r/min, 20/31-p @ 420 r/min). (a) Back EMF waveforms. (b) Harmonic spectra.

TABLE XI Performance of the Four Inner-Rotor FSPM Machines

Single-layer Double-layer Four-layer Distributed 𝜓𝜓𝑝𝑝(Wb) 0.0437 0.0430 0.0426 0.0486 𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐(Nm) 1.02 1.02 1.02 0.75

𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐(Nm) 45.19 44.85 44.36 58.83 𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒 (%) 3.98 3.48 2.77 3.95 𝑃𝑃𝑓𝑓 0.938 0.967 0.970 0.350 𝑃𝑃𝑐𝑐𝑐𝑐(W) 97.92 89.04 89.04 431.11 𝑃𝑃𝑐𝑐𝑐𝑐𝑟𝑟𝑒𝑒(W) 116.13 110.83 105.79 247.79 𝑃𝑃𝑃𝑃𝑃𝑃(W) 86.96 83.06 82.29 182.40 17(%) 90.69 91.14 91.20 75.02

Fig. 19. Variation of torque versus current for the four inner-rotor machines.

The flux-weakening performance parameters of the four inner-rotor machines are listed in Table XII. The torque and power versus speed at the limited voltage of the four machines are shown in Fig. 20(a) and (b), respectively. As can be seen, for the NCWs, a higher number of winding layers indicates lower d-axis inductance, and therefore, worse flux-weakening capability. By contrast, the distributed winding machine has the largest torque capability in the low-speed region if the rated current of 10 A is applied, while it has the best flux-weakening capability in the high-speed region if the reduced current is applied. These results of the inner-rotor FSPM machines are similar to those of the out-rotor FSPM machines.

TABLE XII Flux-Weakening Parameters of the Four Inner-Rotor Machines Single-layer Double-layer Four-layer Distributed 𝑛𝑛𝑏𝑏(r/min) 620 620 620 420 𝑉𝑉𝑝𝑝𝑎𝑎𝑚𝑚(V ) 68.94 66.07 65.19 197.12 𝐿𝐿𝑑𝑑(mH) 1.96 1.61 1.55 13.54 𝐿𝐿𝑞𝑞(mH) 2.25 1.86 1.80 13.74 𝐿𝐿𝑞𝑞/𝐿𝐿𝑑𝑑 1.148 1.155 1.161 1.015 𝑘𝑘𝑓𝑓𝑎𝑎 0.45 0.37 0.36 2.79

Fig. 20. Flux-weakening capability of the four inner-rotor machines. (a) Torque vs. speed. (b) Power vs. speed.

The inductances of the four inner-rotor machines are listed in Table XIII. The profiles of the short-circuit currents in case of a terminal short circuit for the four inner-rotor machines are depicted in Fig. 21. The torque characteristics of the machines after implementation of the fault-tolerant control strategy (see Table VIII) are listed in Table XIV. As can be seen, with the number of winding layers increasing in the NCW machines (from single-layer to double-layer to four-layer), the self-inductance decreases, the short-circuit current increases, the average torque under open-circuit faults is closer to that in its healthy condition, the torque ripple under open-circuit faults reduces. By contrast, the distributed winding machine has the largest self-inductance, the lowest short-circuit current, and the worst torque characteristics under open-circuit faults. These results of the inner-rotor machines are also consistent with those of the out-rotor FSPM machines.

TABLE XIII Inductances of the Four Inner-Rotor FSPM Machines Inductances Single-layer Double-layer Four-layer Distributed 𝐿𝐿𝐴𝐴𝐴𝐴(mH) 3.67 2.39 1.89 10.81 𝐿𝐿𝐴𝐴𝐴𝐴(%) 1.85 0.39 0.08 3.70 𝐿𝐿𝐴𝐴𝐴𝐴(%) 10.35 5.08 20.25 27.02 𝐿𝐿𝐴𝐴𝐴𝐴(% ) 10.35 5.08 20.25 27.01 𝐿𝐿𝐴𝐴𝐴𝐴 (% ) 1.85 0.39 0.08 3.70

Fig. 21. Short-circuit currents versus the variation of the rotor position for the four inner-rotor machines.

TABLE XIV Torque Characteristics of the Four Inner-Rotor Machines In Faulty Conditions Single-layer Double-layer Four-layer Distributed Healthy 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐(Nm) 45.19 44.85 44.36 58.83 𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒(%) 3.98 3.48 2.77 3.95 A Open 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐(Nm) 44.02 (97.41%) 44.39 (98.97%) 44.02 (99.23%) 52.54 (89.31%) 𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒(%) 21.23 18.10 16.81 49.51 A&B Open 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐(Nm) 33.45 (74.02%) 39.00 (86.96%) 40.71 (91.77%) 41.46 (70.47%) 𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒(%) 74.58 44.10 36.54 87.81 A&C Open 𝑇𝑇𝑎𝑎𝑎𝑎𝑐𝑐(Nm) 41.06 (90.86%) 43.13 (96.16%) 43.29 (97.59%) 45.30 (77.00%) 𝑇𝑇𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑙𝑙𝑒𝑒(%) 51.34 31.23 28.57 62.03

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